f(x)-x*f(-x)=x^2

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Solution for f(x)-x*f(-x)=x^2 equation: 


Simplifying
f(x) + -1x * f(-1x) = x2

Multiply f * x
fx + -1x * f(-1x) = x2

Remove parenthesis around (-1x)
fx + -1x * f * -1x = x2

Reorder the terms for easier multiplication:
fx + -1 * -1x * f * x = x2

Multiply -1 * -1
fx + 1x * f * x = x2

Multiply x * f
fx + 1fx * x = x2

Multiply fx * x
fx + 1fx2 = x2

Solving
fx + 1fx2 = x2

Solving for variable 'f'.

Move all terms containing f to the left, all other terms to the right.

Combine like terms: x2 + -1x2 = 0
fx + 1fx2 + -1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(f + fx + -1x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing f to the left, all other terms to the right.

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(f + fx + -1x)' equal to zero and attempt to solve:

Simplifying
f + fx + -1x = 0

Solving
f + fx + -1x = 0

Move all terms containing f to the left, all other terms to the right.

Add 'x' to each side of the equation.
f + fx + -1x + x = 0 + x

Combine like terms: -1x + x = 0
f + fx + 0 = 0 + x
f + fx = 0 + x
Remove the zero:
f + fx = x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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